What's the Benefit of Using Layer Weight?
There are many big differences, among which are that:


Fresnel depends on the face normals of your mesh - it will not work with inconsistent or incorrect normals;
The Layer Weight node allows for a smooth blend between the two;


Depending on what you wish to achieve, it may be better to use a specific one, but generally, you'll want to use the Fresnel node, as it's more physically accurate.